Similarly, some people are better at guessing math sequences - aha, this is double the Fibonacci numbers, this is squares minus one, this sequence is adding 1, then 2, then 3... Simple puzzles; once you know what sort of things to look for, you can solve much faster. The range of exposure to these is what I imagine the Flynn effect to be all about.

Well, that requires one to know wth are the Fibonacci numbers or be able to figure out they follow whatever sequence they do, which is much more likely if someone has been explained the Fibonacci numbers, or at least done math beyond "one, two, many". That's environmental without even needing to be "training to beat the test".